A 3/2 algorithm for two-machine open shop with route-dependent processing times

This paper considers the problem of minimizing the schedule length of a two-machine shop in which not only can a job be assigned any of the two possible routes, but also the processing times depend on the chosen route. This problem is known to be NP-hard. We describe a simple approximation algorithm that guarantees a worst-case performance ratio of 2. We also present some modifications to this algorithm that improve its performance and guarantee a worst-case performance ratio of 3=2.

DFT calculations of the structures and vibrational spectra of the [Fe(bpy)(3)](2+) and [Ru(bpy)(3)](2+) complexes

Structures of the [M(bpy)(3)](2+) complexes (M = Fe and Ru) have been calculated at the B3-LYP/DZVP level. IR and Raman spectra were calculated using the optimised geometries, employing a scaled quantum chemical force field, and compared with an earlier normal coordinate analysis of [Ru(bpy)(3) ](2+) which was based upon experimental data alone, and the use of a simplified model. The results of the calculations provide a highly satisfactory fit to the experimental data and the normal coordinate analyses, in terms of potential energy distributions, allow a detailed understanding of the vibrational spectra of both complexes. Evidence is presented for Jahn-Teller distortion in the E-1 MLCT excited state. (C) 2008 Elsevier B.V. All rights reserved.

Seven 3-methylidene-1H-indol-2(3H)-ones related to the multiple-receptor tyrosine kinase inhibitor sunitinib

The solid-state structures of a series of seven substituted 3-methylidene-1H-indol-2(3H)-one derivatives have been determined by single-crystal X-ray diffraction and are compared in detail. Six of the structures {(3Z)-3-(1H-pyrrol-2- ylmethylidene)-1H-indol-2(3H)-one, C13H10N2O, (2a); (3Z)-3-( 2-thienylmethylidene)-1H-indol-2(3H)-one, C13H9NOS, (2b); (3E)-3-(2-furylmethylidene)-1H-indol-2(3H)-one monohydrate, C13H9NO2 center dot H2O, (3a); 3-(1-methylethylidene)-1H-indol- 2(3H)-one, C11H11NO, (4a); 3-cyclohexylidene-1H-indol- 2(3H)-one, C14H15NO, (4c); and spiro[1,3-dioxane-2,3'-indolin]- 2'-one, C11H11NO3, (5)} display, as expected, intermolecular hydrogen bonding (N-H center dot center dot center dot O=C) between the 1H-indol-2(3H)-one units. However, methyl 3-(1-methylethylidene)- 2-oxo-2,3-dihydro-1H-indole-1-carboxylate, C13H13NO3, (4b), a carbamate analogue of (4a) lacking an N-H bond, displays no intermolecular hydrogen bonding. The structure of (4a) contains three molecules in the asymmetric unit, while (4b) and (4c) both contain two independent molecules.